This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357993 #12 Oct 30 2022 11:01:59 %S A357993 1,2,9,8,17,34,64,129,252,515,1026,2044,4091,8184,16375,32758,65525, %T A357993 131060,262131,524279,1048566,2097167,4194322,8388590,16777203, %U A357993 33554450,67108877,134217712,268435473,536870929,1073741807,2147483622,4294967278,8589934615 %N A357993 a(n) is the unique k such that A357961(k) = 2^n. %C A357993 Conjecture: if we write a(m) = 2^m + d then d < 2*m for m > 2. The reason for this conjecture: the Hamming weight of a number is smaller than its binary logarithm. If we assume in A357961 a random distribution of Hamming weights with values < log_2(k) for A357961(k), then we may expect for each dyadic interval an increase in displacement by the half of the intervals exponent. If we assume instead of randomness a stronger repeating of any Hamming weight, we would even reduce the gained displacement by this. - _Thomas Scheuerle_, Oct 24 2022 %H A357993 Rémy Sigrist, <a href="/A357993/a357993.gp.txt">PARI program</a> %F A357993 Empirically: a(n) ~ 2^n. %e A357993 A357961(1026) = 1024 = 2^10, so a(10) = 1026. %o A357993 (PARI) See Links section. %Y A357993 Cf. A357961. %K A357993 nonn,base %O A357993 0,2 %A A357993 _Rémy Sigrist_, Oct 23 2022